Design of positive, negative, and alternating sign generalized logistic maps
type: Item
instance of: scholarly article
title: Design of positive, negative, and alternating sign generalized logistic maps
zbMATH Open document ID: 1418.39006
DOI: 10.1155/2015/586783
author: Wafaa S. Sayed
author: A. G. Radwan
author: Hossam A. H. Fahmy
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications. This paper investigates a set of four generalized logistic maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications such as quantitative financial modeling. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map. Mathematical analysis for each generalized map includes bifurcation diagrams relative to all parameters, effective range of parameters, first bifurcation point, and the maximum Lyapunov exponent (MLE). Independent, vertical, and horizontal scales of the bifurcation diagram are discussed for each generalized map as well as a new bifurcation diagram related to one of the added parameters. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7025417
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/586783
OpenAlex ID: W1935110352
Wikidata QID: Q59106020
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description: scientific article; zbMATH DE number 7025417